Optical Properties and Raman Scattering of Vanadium Ladder Compounds

Spitaler, Jürgen; Sherman, E. Ya.; Draxl, Claudia; Evertz, Hans Gerd

doi:10.1238/physica.topical.109a00159

Cited by 8 publications

(20 citation statements)

References 9 publications

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“…Due to the asymmetric crystal environment of the V ions in NaV 2 O 5 , the strongest lattice coupling is a Holstein-like electron-phonon interaction involving the d xy electrons. 20,24 We investigate the extended Hubbard model with Holstein coupling, introduced in Ref. 23, using high precision Density Matrix Renormalization Group (DMRG) calculations on isolated and on two coupled ladders.…”

Section: 17mentioning

confidence: 99%

“…1. The parameters are taken from LDA calculations 24 ; the hopping amplitudes t ij are compatible with earlier calculations. 25,39 The lattice parameters C and κ were extracted by comparing the total energy and the inter-ionic forces in distorted and undistorted lattices.…”

Section: Modelmentioning

confidence: 99%

“…24,25,39 The Coulomb repulsion is very difficult to compute; estimates in the literature vary strongly. 9,17,28,29,30,40 In our study, we take V a = V b = V ab = V for simplicity, and investigate the model as a function of V .…”

Section: Modelmentioning

confidence: 99%

“…6(b) for V * = 1.3 t a . Since estimates of the interladder hopping t ab in NaV 2 O 5 vary, 24,25,39 we have performed our calculations for two values, t ab = 0.17 t a and 0.33 t a . At t ab = 0.17 t a , the spin gap for two coupled ladders both with and without lattice distortion is similar in value and finite-size behavior to that for the isolated ladder, which vanishes in the thermodynamic limit.…”

Section: Coupled Laddersmentioning

confidence: 99%

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Charge order induced by electron-lattice interaction inNaV2O5

2005

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We present Density Matrix Renormalization Group calculations of the ground-state properties of quarter-filled ladders including static electron-lattice coupling. Isolated ladders and two coupled ladders are considered, with model parameters obtained from band-structure calculations for α ′ -NaV2O5. The relevant Holstein coupling to the lattice causes static out-of-plane lattice distortions, which appear concurrently with a charge-ordered state and which exhibit the same zigzag pattern observed in experiments. The inclusion of electron-lattice coupling drastically reduces the critical nearest-neighbor Coulomb repulsion Vc needed to obtain the charge-ordered state. No spin gap is present in the ordered phase. The charge ordering is driven by the Coulomb repulsion and the electron-lattice interaction. With electron-lattice interaction, coupling two ladders has virtually no effect on Vc or on the characteristics of the charge-ordered phase. At V = 0.46 eV, a value consistent with previous estimates, the lattice distortion, charge gap, charge order parameter, and the effective spin coupling are in good agreement with experimental data for NaV2O5.

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Section: 17mentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: Coupled Laddersmentioning

confidence: 99%

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Charge order induced by electron-lattice interaction inNaV2O5

2005

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“…A zigzag charge order as observed in NaV 2 O 5 [4] is already created in this model by the nearestneighbor Coulomb repulsion V for an isolated ladder, but only at overly large values of V [5-10]. In a recent DensityMatrix Renormalization Group (DMRG) study [8], we showed that the inclusion of a strong effective Holstein coupling to the lattice, which was found in local-density approximation (LDA) calculations [11], reduces the required Coulomb repulsion to a realistic value. The DMRG calculations then yielded good agreement between theoretical and experimental results for the amount of charge order, the extent of lattice distortion in the c direction, the effective spin coupling J eff in the b direction, and the charge gap.…”

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confidence: 92%

Creation and Destruction of a Spin Gap in Weakly Coupled Quarter-Filled Ladders

2006

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We investigate weakly coupled quarter-filled ladders with model parameters relevant for NaV(2)O(5) using density-matrix renormalization group calculations on an extended Hubbard model coupled to the lattice. NaV(2)O(5) exhibits super-antiferroelectric charge order with a zigzag pattern on each ladder. We show that this order causes a spin dimerization along the ladder and is accompanied by a spin gap of the same magnitude as that observed experimentally. The spin gap is destroyed again at large charge order due to a restructuring of the spins. An analysis of an effective spin model predicts a recreation of the gap by interladder singlets when the charge order increases further.

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Finite-temperature investigation of quarter filled ladder systems

Gabriel

Sherman

Lang

et al. 2005

Physica B: Condensed Matter

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We investigate charge ordering in a quarter-filled ladder at finite temperature by determinantal Quantum Monte Carlo. The sign problem is moderate in a wide range of model parameters relevant for NaV2O5. The charge order parameter exhibits a crossover as a function of inverse temperature β on finite systems. Above a critical nearest neighbor Coulomb repulsion Vc, the correlation length grows exponentially with β, indicative of the ordered phase at β = ∞. We find a clear single-particle gap manifesting itself in a flat n(µ) dependence at large nearest neighbor Coulomb repulsion V . Key words:quarter-filled ladders, charge ordering, quantum Monte CarloThe inorganic ladder compound NaV2O5 has attracted great attention in recent years. This interest was triggered by magnetic susceptibility measurements [1], which show a phase transition at T = 34 K into a low-temperature spin-gapped phase. This transition is accompanied by charge ordering, as observed in NMR measurements [2], where the valence of the vanadium sites changes from V 4.5 to V 4.5±δ , with δ the amount of charge disproportion. This transition has been studied theoretically by several techniques at T = 0 [3].On a microscopic level the system can be described by an extended Hubbard modelat quarter filling n = 0.5, with hopping matrix elements tij = tx along the ladder and tij = ty within a rung, and chemical potential µ. We state all energies in units of ty. These hopping parameters as well as the onsite Coulomb interaction can be extracted from firstprinciple calculations [4]. The hopping along chains * Corresponding author: e-mail: evertz@tugraz.at tx ≃ 0.5ty is weaker than along rungs. This strongly influences the physics of the ladder, for which a spingap seems to appear at tx > ∼ ty [3]. We used tx = 0.5 and U = 8. Since the non-local Coulomb interaction V cannot be determined properly by band-structure calculations, we used V as a free parameter of the Hamiltonian. The charge order parameter is ∆ 2 co = 1 2L n ij e iQ(r i −r j ) (ni − n )(nj − n ) with Q = (π, π), which is unity for complete ordering.We performed grand canonical calculations by determinantal quantum Monte Carlo. These are often very difficult for doped systems because of a sign problem. Fortunately, the average sign is favorably large in the relevant parameter range of tx/ty = 0.5 and large V (Fig. 1). In the opposite case of isotropic tx = ty at small V , sign becomes very small. The charge order parameter exhibits similar behavior, but it is less strongly dependent on tx/ty. Charge order grows with increasing V . Fig. 2 shows the charge correlation length ξcc. At small interactions, V = 1.5 and 2.0, the correlation length seems to saturate, but for V = 2.5 and 3.0 it increases exponentially with β, with a V -dependent slope. This behavior is consistent with the 1D Ising model in a transverse field (IMTF) [5], which is equiv-

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Optical Properties and Raman Scattering of Vanadium Ladder Compounds

Cited by 8 publications

References 9 publications

Charge order induced by electron-lattice interaction inNaV2O5

Charge order induced by electron-lattice interaction inNaV2O5

Creation and Destruction of a Spin Gap in Weakly Coupled Quarter-Filled Ladders

Finite-temperature investigation of quarter filled ladder systems

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